Communications in Mathematical Sciences
Volume 17 (2019)
Consistent mean field optimality conditions for interacting agent systems
Pages: 1095 – 1108
We are interested in the derivation of optimality conditions for controlled interacting agent systems. We establish the relation between mean field optimality conditions and the optimality condition of the mean field control problem. This link is important for many recently published articles on control strategies for agent based systems since it establishes the precise relation between multipliers for the individual agents and the probability density distribution of the multipliers in the mean field limit. The relation to different notions of differentiability are also shown.
kinetic equations, particle systems, optimal control, meanfield limits
2010 Mathematics Subject Classification
49J15, 49J20, 82B40
This work has been supported by NSF RNMS grant No. 1107291 (KI-Net) and DFG HE5386/14-15, BMBF 05M18PAA, DFG-GRK 2326 and ID390621612 Cluster of Excellence Internet of Production (IoP).
Received 29 November 2018
Accepted 1 May 2019
Published 25 October 2019